Inertial navigation systems (INSs) have the well-known advantages of being self-contained, weatherproof, jam-proof, and non-self-revealing while providing stable navigation information with little high-frequency noise. However, their single most important drawback is the growth of their error cumulatively with time in an unbounded manner. Navigation systems based on position fixing, in contrast, offer bounded errors in the long term, but their output is usually contaminated with strong high-frequency noise. To harness the advantages of both types of systems, INSs have been traditionally aided or augmented by one or more fixing system(s). Such an arrangement preserves the excellent short-term stability and damping (i.e. high-frequency rejection) capability of INSs while limiting its long-term drift. In recent years, the availability of navigation information from the Global Positioning System (GPS) reliably and accurately over the entire globe has made it a natural choice as the means of augmentation of INSs. An integrated navigation system combining data from two or more ‘pure’systems is called a hybrid navigation system (HNS).
There is no unique way of combining navigation information from the INS and GPS. Depending on the goals and specifications of the overall navigation system, the instrument and equipment available, cost constraints, and technology options, the scheme for integrating INS and GPS may take one of many forms. In generic terms integration of diverse ‘pure’ navigation systems can be performed at various levels. At the simplest and most basic level, each system may be allowed to run independently, generating its own navigation data separately which may then be combined periodically to reset any accumulated error. At the other extreme, the two (or more) systems may be intimately coupled right at their raw data levels in a quasi-continuous manner with the intention of maximising their mutually beneficial effect and deriving the ‘best’ possible navigation information.
Hybrid navigation architectures have been a subject of much research and development, and a significant body of information is available on the subject. However, there are clear gaps in open literature on many practical issues that arise in the context of implementing specific HNSs. In this thesis we investigate the architecture, implementation and performance issues of HNSs that combine stand-alone INS and GPS units.
The thesis consists of eight chapters. The first chapter offers an introduction to the navigation problem and discusses the basic types of navigation including inertial and satellite navigation. Inertial sensors such as gyroscopes and accelerometers and the GPS are discussed in some detail. The types and principle of gyroscopes and accelerometers and the error sources in inertial navigation are briefly covered, as also the advantages and disadvantages of INS and the trends in inertial system development.The chapter also touches upon GPS segments (space, control and user), the theory and determination of position fix, and the GPS error sources. Mention is also made of the types of GPS receiver available and the trends in GPS technologies. Integration of INS and GPS and its benefits are discussed and a set of specifications for an integrated system is laid out to serve as the basis for the configurations proposed later.
The second chapter, in its three sections, provides a summary of the significant literature relevant to INS and GPS in the context of their integration.
Chapter three discusses mechanisation aspects of the INS-GPS hybrid navigation system. This chapter is divided into three sections. In the first section the frames of reference, INS mechanisation and the error equations are discussed. The definitions for the various frames such as body, platform, local level, geodetic, Earth-centred-Earth-fixed (ECEF), and the computer frame are mentioned along with the direction cosine matrices for the transformation of frames. In the second section various types of mechanisation of INS and the summary of tilt, velocity and position equations are described. The INS can be mechanised in two ways: the stable platform and the strap-down. In this chapter the general error equations for platform tilt, velocity and position are listed. Platform-based systems can be mechanized as one of the following types, viz. unipolar, Focualt, north pointing and wander azimuth. The definitions and summary of the tilt, velocity and position, and the error equations are given for all these types of mechanization. The accelerometer and gyro error models are discussed. It is pointed out that inclusion of all the possible INS states in the model would lead to a 45-state system which would be too complex to handle on board. The scope for reduction of model order and the effect of such reduction are brought out. The section ends with a summary of the INS error equations considered for implementation. In the third section the GPS principle and derivation of navigation solutions based on GPS measurements are dealt with. GPS error modelling, computation of DOP (dilution of precision), and clock modelling are also discussed. In this section the navigation solution for various classes of users – stationary, low-dynamics, medium-dynamics and high-dynamics – are discussed. The INS model and the clock model defined in this chapter are used in configuring the integrated system model later.
Chapter four discusses the various HNS configurations and their implementation to mitigate the INS error. Three levels of integration are considered:
a. Output coupled: The INS needs initial alignment during which the INS position and velocity are initialised with the precisely known co-ordinates and components at the starting location. Starting with these initial conditions, the INS-sensed accelerations are continuously integrated to yield the current velocity and position. As mentioned earlier, the INS error is dependent on this initial value and further increases with time. If the initial position and velocity inputs are precise, the short-term INS accuracy (typically for the first 10-15 minutes in case of aircraft) is usually within acceptable limits. Further error built up during longer flights can be reduced by periodic updation of INS with the precise position and/or velocity values. To achieve this the pilot may, for example, fly over waypoints whose co-ordinates are precisely known. This would constitute a physical or manual method of INS re-initialisation. A better and more modern method is to use precise GPS-derived information to reinitialise the INS periodically and automatically.
b. Medium coupled: Another way of mitigating the INS error build-up is by using medium-coupled HNS wherein the INS errors are estimated using the GPS measurements as reference. The INS outputs are corrected by applying these error estimates. The important point to note here is that in medium coupling, the errors in the INS states are considered instead of the states themselves. The final geodetic outputs from the two systems are used as measurements. A twelve-state indirect feed-forward Kalman filter is used to estimate the INS position error.
c. Tightly coupled: The basic measurements from the GPS are pseudoranges which are the distances from the user to the GPS satellites. By making a minimum of four such measurements the GPS receiver computes the user location in the geodetic coordinates. Conversely, knowing the user position from INS, it is possible to calculate the expected pseudoranges to known GPS satellite locations. Comparing the measured and the computed pseudoranges, the filter estimates the errors in the INS position. In this work a seventeen-state, feed-forward, indirect Kalman filter is configured to estimate the INS-derived pseudorange errors. These errors are then translated into positional errors which are used to correct the indicated INS positions.
In configuring the filter it is assumed that the INS and GPS are physically separated and data transfer is through the interface buses. In this chapter the simulators used for validation and performance estimation of the configurations are also described. Two simulators are used to validate the hybrid system, namely, software-and hardware-based simulators. The simulators simulate the six-degree-of-freedom of trajectory generator, and error models of INS and GPS. The truth data from the trajectory generator are combined with the INS error and GPS error to get the INS and GPS outputs respectively.
The fifth and sixth chapters covers the validation of the above-mentioned three configurations. Since analysis of output coupled systems is rather straightforward, simulation and validation of the configuration are carried out for the medium and tightly coupled systems Covariance analysis and Error analysis modes of simulation are carried out to study and validate the behaviour of the configurations. In covariance analysis one obtains the root mean square (rms) value of the errors obtained from several Monte Carlo runs. It gives an estimate of the lower bound of the system errors. Covariance simulation provides a degree of confidence in the error model but is generally not sufficient to expose the complete behaviour of the system. For detailed investigation, error simulation needs to be carried out for the entire navigation system. In the thesis, covariance simulation is carried out for both the configurations to check the sensitivity of the system to measurement update rates, process noise, update times for the transition matrix, and also for the validity of the truncation of the Taylor series expansion. The details of the simulation processes and their results are discussed in these chapter.
The seventh chapter makes a performance comparison of the configurations and draws inferences for practical hybrid system implementation. From the comparisons it is seen that the loosely coupled configuration is the simplest. In this configuration there is no requirement of the Kalman filter. The accuracy depends on the update rate. If the position update is made, for example, once every 600 s then the error in the combined system will be limited to the sum of the error due to the GPS and that accumulated in the INS alone over the of 600 s interval. There is no coordinate transformation required. In the case of medium coupled filter the addition of process noise to the GPS clock model is not critical. The position accuracy achieved is around 2 m (rms). The coordinate transformations are only from the body to platform, and platform to geodetic axes. The observation matrix is very simple in this case and the computation burden is low. Dynamic tuning of the measurement matrix is not required in real time.In the case of tightly coupled configuration the addition of a certain amount of process noise deliberately to the GPS clock model is critical. The position accuracy achieved with tight coupling is around found to be 34 m (rms) without the addition of process noise. On addition of a controlled amount of noise to the GPS clock bias and clock drift states and inclusion of measurement noise as a function of GPS signal strength, the position accuracy improves significantly, to about 7m (rms). Figures 2a and 2b below depict the behaviour before and after inclusion of the noise. The coordinate transformations are from body to platform, platform to geodetic, and geodetic to ECEF coordinates, and vice versa. The observation matrix (H) for this integration model is very complicated, and the computational burden is very high. In this configuration H transfers the measurements from metres to radians. Dynamic tuning of measurement matrix is required in this case.
Chapter eight of the thesis summarises the results and lists out the conclusions arrived at from the study. It also includes a section with suggestions for future work in this direction.